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A043547 Odd numbers interspersed with double the previous odd number. 10
1, 2, 3, 6, 5, 10, 7, 14, 9, 18, 11, 22, 13, 26, 15, 30, 17, 34, 19, 38, 21, 42, 23, 46, 25, 50, 27, 54, 29, 58, 31, 62, 33, 66, 35, 70, 37, 74, 39, 78, 41, 82, 43, 86, 45, 90, 47, 94, 49, 98, 51, 102, 53, 106, 55, 110, 57, 114, 59, 118, 61, 122, 63, 126, 65, 130, 67, 134 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

As pointed out by E. Angelini on the SeqFan list (cf. link), this is the lexicographically earliest sequence of positive integers without repetitions such that the sum of four consecutive terms is always a multiple of 4. - M. F. Hasler, Mar 22 2013

LINKS

Table of n, a(n) for n=1..68.

E. Angelini, k-chunks sum and division by k, post to the SeqFan list, Mar 22 2013

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

FORMULA

a(n) = (2 - n) * (n - floor(n/2) * 2) + 2 * (n - 1).

G.f.: x*(1+2*x)*(1+x^2)/(1-x^2)^2. - Ralf Stephan, Jun 10 2003

a(2n-1) = 2n-1, a(2n) = 4n-2. - M. F. Hasler, Mar 22 2013

From Wesley Ivan Hurt, Nov 22 2015: (Start)

a(n) = 2*a(n-2) - a(n-4) for n>4.

a(n) = n*(-1)^n/2 - (-1)^n + 3*n/2 - 1. (End)

EXAMPLE

a(1)=1 because n is odd. a(2)=2 because a(1)*2=2.

MAPLE

A043547:=n->n*(-1)^n/2-(-1)^n+3*n/2-1: seq(A043547(n), n=1..100); # Wesley Ivan Hurt, Nov 22 2015

MATHEMATICA

Flatten[Table[Accumulate[{2 n - 1, 2 n - 1}], {n, 40}]] (* Wesley Ivan Hurt, Nov 22 2015 *)

With[{o=Range[1, 71, 2]}, Riffle[o, 2o]] (* Harvey P. Dale, Sep 17 2019 *)

PROG

(PARI) A043547(n)=n+!bittest(n, 0)*(n-2) \\ M. F. Hasler, Mar 22 2013

(MAGMA) [n*(-1)^n/2-(-1)^n+3*n/2-1 : n in [1..50]]; // Wesley Ivan Hurt, Nov 22 2015

(PARI) Vec(x*(1+2*x)*(1+x^2)/(1-x^2)^2 + O(x^100)) \\ Altug Alkan, Nov 22 2015

CROSSREFS

For n>3, a(n) = A059029(n-3)+3. For n>1, a(n) = A022998(n-2)+2.

Sequence in context: A091239 A145110 A257405 * A338702 A064919 A064923

Adjacent sequences:  A043544 A043545 A043546 * A043548 A043549 A043550

KEYWORD

easy,nonn

AUTHOR

Jim Cook (jcook(AT)halcyon.com), Mar 01 2000

EXTENSIONS

More terms from James A. Sellers, Mar 01 2000

STATUS

approved

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Last modified January 26 07:32 EST 2022. Contains 350577 sequences. (Running on oeis4.)